There is no such thing as a general 'minimum' surface interval. I haven't found any computer that comes with such a function. It depends on the time and your depth of your next dive and your divecomputer (obviously) doesn't know that.
Most computers do offer a 'plan' mode where you can find the maximum non-deco-limit (NDL) GIVEN your previous dive(s) and your current surface interval and the maximum depth of your next dive.
For a 'normal' dive, you can surface 'directly'. From there on, the longer you stay at the surface, the more N2 you lose and the longer you can stay down again (roughly) on a second dive. If you plunge in just after (ie) half an hour (assuming you stayed well within the recreational limits in your previous dives), you haven't released much of the N2 in your tissues yet and you hit any non-deco-limits much sooner. The longer you want to stay down on your next dive, the longer you have to wait at the surface. Just wait until your divecomputer in plan mode gives the NDL-time you desire at the depth you punch in.
Modern insights show (however) that many compression/decompression cycles in a relative short time are bad for your body. This has something to do with how bubbles form in your body and how certain tissues react to pressure changes. That's why a certain minimum interval is very advisable!!! Many divecomputers also take this into account and give shorter NDL times.
Decompression theory is not an 'absolut' business (although the companies want you to beleive otherwise ofcourse). It is still is a model that proved to be safe for 'most of the people'. But it doesn't actually measure anything in your body, nor take into account your physical condition, water temperature, dehydration etc, while these things certainly influence you N2 offgasing and how your body reacts. It is still a model that is (by definition) always incomplete.
Your divecomputer is just a 'hint' (a very good one but still), nothing more. It's always a good idea to stay well within the limits.
To recapitulate:
Use your plan mode on your computer instead to find out when you are able to make your next dive. And you always want to and always take a certain minimum interval into account between dives.